8 C. V. L. CHARLIER, 
The values of w', v'! and W, as well as those of the direction 
cosines y,, are known for each star. Applying the method of least 
squares, we are now able from each one of the equations (3) to de- 
termine the mean values of U", V". W" — that is the mean velocity 
of the B-stars referred to the sun. The third equation gives the value 
of U", V", W" expressed in linear measure (Siriometers per stellar 
year); from the two first equations the same velocity components are 
expressed as functions of R. Comparing with the former results we 
get the value of À. 
It R cannot be considered a constant the two first equations (3) 
give us not the mean values of U", V", W" but the mean values of 
1 ini I 11 1 I! 
R De: Min, 
and a comparison with the result of the radial velocity equation now 
gives the mean value of 1: &. 
The value of R being known we get the distance of each indi- 
vidual star from (1), and from (5) the values of the velocity compo- 
nents perpendieular to the line of sight. "Through an inversion of (5) 
we finally get velocity components in the equator system. 
5. Let any one of the equations (3) be written in the form 
n = ax + by + 
then the normal equations are 
(an) = (aa) x + (ab) y 3- (ac) 2 , 
(6) (bn) = (ba) x + (bb) y + (be)z , 
(cn) = (ca) x + (cb) y + (cc) 2 
Consider now the determinant 
Di (nn), (na), (nb), (ne) 
(an), (aa), (ab). (ac) 
(bn), (ba), (bb), n 
I (en) > (ca), (cb), | 
1 [ shall call w and » the reduced proper motions of the stars. 
